Quasi-hereditary algebras and directed corings

Quasi-hereditary algebras are abundant in representation theory. Classical examples include blocksof BGG category O associated to a complex simple Lie algebra and Schur algebras of symmetricgroups. Generalising the situation for complex simple Lie algebras, Koenig introduced the notion ofan exact Borel subalgebra of a quasi-hereditary algebra. Given a quasi-hereditary algebra A with anexact Borel subalgebra B, one can form the dual coring Hom(A,B). In this talk we will discussexistence and uniqueness of exact Borel subalgebras and explore the relationship betweenquasi-hereditary algebras and their dual corings. This includes joint work with S.Koenig, S.Ovsienko,A.Bodzenta, V.Miemietz, and T.Brzezinski.